The Powell family and the Tanaka family each used their sprinklers last summer. The water output rate for the Powell family's sprinkler was 25L per hour

Question

The water output rate for the Tanaka family's sprinkler was 20L per hour. The families used their sprinklers for a combined total of 35 hours, resulting in a total water output of 775L. How long was each sprinkler used in hours?

Answer 1

First, write down all your knowns :

Subscript P (_p) denotes Powell Family

Subscript T (_T) denotes Tanaka Family

Rate_P = R_P = 25 L/hr

R_T = 20 L/hr

Volume = V = R*T

Volume (all) = V_A = R_P*T_P + R_T*T_T = (25 L/hr)*T_P + (20 L/hr)*T_T = 775 L

Time (all) = T_A = 35 hr = T_P + T_T

We have 2 equations and 2 unknowns. This problem is solvable as is.

Next, you solve for one variable using the easier of the equations :

35 hr = T_P + T_T

35 hr - T_T = T_P

Next you plug in that solved variable into the other equation (not the one used in the last step)

(25 L/hr)*T_P + (20 L/hr)*T_T = 775 L

(25 L/hr)*(35 hr - T_T) + (20 L/hr)*T_T = 775 L

Solve

(25 L/hr)*(35 hr - T_T) + (20 L/hr)*T_T = 775 L

875L - (25 L/hr)(T_T) + (20 L/hr)*(T_T) = 775 L

875L - (5 L/hr)(T_T) = 775 L

-(5 L/hr)(T_T) = -100 L

T_T = (-100L) / (-5 L/hr)

T_T = 20 hr

Next plug that solved variable into either equation (pick the easier equation)

35 hr = T_P + T_T

35 hr = T_P + 20 hr

15 hr = T_P

T_P = 15 hr

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Always check your work!

Volume (all) = V_A = R_P*T_P + R_T*T_T = (25 L/hr)*T_P + (20 L/hr)*T_T = 775 L

(25 L/hr)*(15 hr) + (20 L/hr)* (20hr) = 775 L

375 L + 400 L = 775 L

775 L = 775 L CORRECT!!

Time (all) = T_A = 35 hr = T_P + T_T

35 hr = 15 hr + 20 hr

35 hr = 35 hr CORRECT!!